\begin{problem}{Guards}{guards.in}{guards.out}{1 second}{32 megabytes}

Near a military base there is a system of trenches, modeled as line segments on a plane. During 
nighttime, when most soldiers are fast asleep, three guards stand watch of the trenches. Two 
guards can see each other if there is a trench (or a row of trenches) along the entire straight 
line segment between them and there is no third guard on that line segment.

For security reasons, the guards must be placed so that each guard sees the other two. How many 
ways can they be placed?

\InputFile

The first line contains the integer $N$ ($1 \le N \le 20$), the number of trenches. Each of the 
next $N$ lines contains the description of one trench: four positive integers $X_1$, $Y_1$, 
$X_2$, $Y_2$ (all less than or equal to $1\,000$), where $X_1$ and $Y_1$ are coordinates of 
one end, while $X_2$ and $Y_2$ are coordinates of the other end of the trench.

Trenches in the input may overlap and share endpoints.

\OutputFile

Output on a single line the number of ways the guards can be placed.

\Example

\begin{example}
\exmp{
6
0 0 1 0
0 0 0 1
1 0 1 1
0 1 1 1
0 0 1 1
1 0 0 1
}{
8
}%
\exmp{
4
5 1 7 1
1 1 5 1
4 0 4 4
7 0 3 4
}{
1
}%
\exmp{
3
2 2 3 2
3 2 3 3
3 3 2 3
}{
0
}%
\end{example}

\end{problem}